CN110208769B - Ray tracing method and system based on NURBS curved surface - Google Patents
Ray tracing method and system based on NURBS curved surface Download PDFInfo
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- CN110208769B CN110208769B CN201910604272.5A CN201910604272A CN110208769B CN 110208769 B CN110208769 B CN 110208769B CN 201910604272 A CN201910604272 A CN 201910604272A CN 110208769 B CN110208769 B CN 110208769B
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/411—Identification of targets based on measurements of radar reflectivity
Abstract
The invention discloses a ray tracing method and system based on NURBS (non-Uniform rational B-spline), which mainly solve the problems of low speed and low precision of the existing ray tracing method. The scheme is as follows: 1. representing the curved surface into a plurality of curved surface elements according to the curved surface node distance information; 2. arranging a bounding box by using coordinate axes of the curved surface elements, and excluding a part of curved surface elements without intersection points; 3. utilizing a triangular surface element control network of the curved surface to further exclude curved surface elements without intersection points; 4. an extremum search iteration method is applied to obtain the intersection point of the ray and the residual surface element; 5. and tracking the rays by using a geometrical relation and a Fresnel law to form a recursion, and realizing ray trajectory tracking. According to the method, more non-intersection surface elements are eliminated through the coordinate axis arrangement bounding box and the triangular surface element control network, ray tracing time is reduced, ray-surface intersection points are solved through extremum search iteration, intersection point precision is improved, and the method can be used for quickly and accurately calculating the radar scattering cross section area of the surface curved target.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a ray tracing method which can be used for accurately calculating a radar scattering cross section RCS of a curved object.
Background
When the radar scattering cross section of the target is calculated, the scattering field of the target not only comprises the field generated by primary scattering, but also comprises the field generated by multiple scattering. Calculating a scattered field generated by electromagnetic waves after multiple reflections on the target surface requires applying a bounce ray method SBR, and ray tracing is the essential content of the algorithm. For the case of curvature of the target surface, a large number of small-sized triangular plane elements are generally used to approximate the target surface, which may distort the model of the target itself, and the influence of curvature is ignored in the ray tracing process, thereby artificially distorting the calculation result. The SBR algorithm based on the non-uniform rational B-spline NURBS surface modeling solves the problem, and can calculate the multiple scattering fields of the surface of any curved target. At present, the ray tracing method based on the curved surface is finally attributed to a complex mathematical formula, and for the processing of the mathematical formula, a Newton iteration method is mostly adopted.
The Newton iteration method solves the mathematical formula by subdividing the curved surface in various complex ways, so that at most one intersection point exists in the subdivided curved surface elements, then the curved surface elements are used as iteration areas, strict iteration initial values are obtained by using complex means, the iteration process is started after the preparation work is done, and the obtained result is used as a new iteration value to carry out the next iteration until the iteration termination condition is met. Newton's iterative method has a number of drawbacks: first, the preliminary preparation work takes a lot of time since it is ensured that there is at most one intersection in the iteration region. Secondly, because the Newton iteration method has strict requirements on the initial value, if the initial value is not properly selected, wrong intersection points or convergence can be iterated, intersection point omission or errors are caused, so that the tracking of some effective rays is judged to be invalid, and the RCS calculation accuracy is not high; the result of the iteration process may cross the boundary of the iteration region, and thus the initial iteration value needs to be reselected and the iteration is performed again, so that the time consumption of ray tracing is increased, and the overall calculation of the target RCS becomes complicated.
Disclosure of Invention
The invention aims to provide a ray tracing method and system based on a NURBS curved surface aiming at the defects of the existing method, so as to effectively find out proper initial values and iteration regions, simplify the iteration process, obtain more accurate line-surface intersection points, reduce ray tracing time and improve RCS calculation accuracy.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
1. a NURBS surface-based ray tracing system, comprising:
the first-stage rejection detection module is used for constructing a respective coordinate axis arrangement bounding box AABB for each curved surface element, if a ray does not intersect with a certain AABB, the ray does not have an intersection point with the curved surface element corresponding to the AABB, the curved surface elements contained in the AABB are excluded, and the reserved curved surface elements are determined as an initial curved surface element set;
the second-stage rejection detection module (2) is used for establishing respective triangular surface element control networks for the surface elements in the initial surface element set, if the ray does not intersect with a certain triangular surface element control grid, the ray does not have an intersection point with the surface element corresponding to the triangular surface element control grid, the surface element corresponding to the control network is excluded, and the reserved surface elements are determined as a target surface element set;
the line-curved surface intersection detection module (3) is used for solving the intersection points of the curved surface elements and the rays corresponding to the triangular surface element control network in an iterative manner by using an extremum search method, namely, according to the number k of the intersection points of the rays and the triangular surface element control network, and then combining the properties of non-uniform rational B spline NURBS (non-uniform rational B spline) to obtain an initial value and an iterative area matched with the extremum search method, and then using the obtained initial value and the iterative area to solve the intersection points of the curved surface elements and the rays corresponding to the triangular surface element control network in an iterative manner by using the extremum search method;
and the track tracking module (4) is used for selecting the illumination intersection point closest to the ray source point, obtaining the reflection direction of the ray by applying Fresnel law, taking the obtained intersection point as a starting point, taking the reflected ray as a new incident ray to continue tracking, and forming recursion, thereby realizing the ray track tracking.
2. A ray tracing method based on a NURBS curved surface comprises the following steps:
1) According to the nodal distance information of the non-uniform rational B-spline NURBS curved surface, the NURBS curved surface is represented as a plurality of connected NURBS curved surface elements;
2) Establishing a coordinate axis arrangement bounding box AABB (array of bounding boxes) for each curved surface element by utilizing the strong convex hull property of the NURBS curved surface element, if an incident wave ray does not intersect with the AABB bounding box, the ray does not have an intersection point with the curved surface element corresponding to the AABB bounding box, excluding the curved surface elements contained in the AABB bounding box, and determining the reserved curved surface elements as an initial curved surface element set;
3) Establishing respective triangular surface element control networks by utilizing control vertexes of all surface elements in the initial surface element set, if an incident wave ray does not intersect with a certain triangular surface element control grid, the ray does not have an intersection point with the surface element corresponding to the triangular surface element control grid, excluding the surface element corresponding to the control network, and determining the reserved surface element as a target surface element set;
4) Obtaining an intersection point of a certain incident wave ray and a certain surface element by using an extremum search iteration method:
4a) Obtaining the number k of intersection points of the triangular surface element control network corresponding to the rays and the curved surface element by using an intersection testing method of the rays and the planar element, wherein k is less than or equal to 2;
4b) According to different conditions of k, combining the property that the NURBS surface elements have the highest continuity in the node distance, determining an iteration area and an initial iteration value which are matched with an extremum search method:
4b1) When k =1, the ray and the surface element have at most one intersection point, and the parameter domain of the surface element is directly used as an iteration domain [ u [ u ] ] i ,u i+1 )×[v j ,v j+1 ) Center of parameter domain
As initial iteration values, wherein u and v are two parameters of the NURBS curved surface, 0 is equal to or less than u, v is equal to or less than 1, subscripts i and j represent node coordinates of the parameters, 0 is equal to or less than i is equal to or less than n-1,0 is equal to or less than j is equal to or less than m-1, n, m is u, the number of B spline basis functions in the v direction is [. Cndot.) represents a node distance, and [. Cndot. ] represents a parameter element consisting of the node distances in the two directions;
4b2) When k =2, the parameter domain of the surface element needs to be subdivided and then iterated: equally dividing the parameter domain of the curved surface element into four regions respectively as iteration regions, and taking the parameter values of the midpoints of the four regions as initial iteration values;
4c) According to the obtained initial iteration value and the iteration area, an extremum searching method is applied to iteratively solve the intersection point of the ray and the curved surface element corresponding to the triangular surface element control network;
5) According to 4) the method for obtaining the intersection point of a certain incident wave ray and a certain curved surface element, obtaining all intersection points of the ray and all curved surface elements forming a target, then obtaining an illuminated intersection point closest to a ray source point by utilizing a geometric relation, obtaining the reflection direction of the ray by applying a Fresnel law, taking the illuminated intersection point as a starting point, taking the reflected ray as a new incident ray to continuously track, forming a recursion, and realizing ray trajectory tracking.
Compared with the prior art, the invention has the following advantages:
1. the ray tracing time is short.
Because the non-uniform rational B-spline NURBS has less geometrical information, the traditional intersection point positioning is only limited to establishing AABB (architecture analysis and bounding table) for the curved surface elements, and invalid curved surface elements cannot be removed too much, so that a plurality of invalid line-plane intersection calculations exist. In order to remove more invalid surface elements, more effectively position intersection points and reduce ray tracing time, the invention fully utilizes the geometric information and properties of NURBS, removes more invalid surface elements by establishing a triangular surface element control network, saves more redundant line-plane intersection calculation and further reduces the ray tracing time.
2. RCS has high calculation precision.
For line-plane intersection calculation, the traditional Newton iteration method has strict requirements on initial values, intersection points are omitted or wrong intersection points appear due to improper selection, and RCS calculation is distorted. According to the method, the initial value and the iteration area matched with the extremum search method are obtained according to the number k of the intersection points of the rays and the triangular surface element control network and by combining the property of the NURBS, then the extremum search method is applied to solve the intersection points in an iteration mode, the intersection point precision is improved, and the RCS calculation precision is further improved.
Drawings
FIG. 1 is a system diagram of the present invention;
FIG. 2 is a flow chart of an implementation of the method of the present invention;
FIG. 3 is a diagram illustrating the mapping of a surface parameter domain to an actual domain according to the present invention;
FIG. 4 is a schematic diagram of the AABB structure of the surface element of the present invention;
FIG. 5 is a schematic diagram of a triangular surface element control network of a surface element according to the present invention;
FIG. 6 is a schematic diagram of the iterative region partition in the present invention;
FIG. 7 is a diagram of a model of an object being ray traced using the method of the present invention;
FIG. 8 is a graph of the scattering results obtained after ray tracing a flat panel model using the method of the present invention.
Detailed Description
Embodiments and effects of the present invention will be described in further detail below with reference to the accompanying drawings.
Referring to fig. 1, the system of the present invention includes a first-level rejection detection module 1, a second-level rejection detection module 2, a line-curved surface intersection detection module 3 and a trajectory tracking module 4, and the specific contents of each module are as follows:
the first-stage rejection detection module 1 is configured to construct a coordinate axis arrangement bounding box AABB for each curved surface element by using a strong convex hull property of a non-uniform rational B-spline NURBS curved surface element, wherein the AABB completely contains the corresponding curved surface element, if a ray does not intersect with a certain AABB, the ray does not have an intersection point with the curved surface element corresponding to the AABB, the curved surface element contained by the AABB is excluded, all curved surface elements in the AABB which do not intersect with the ray are firstly excluded by using a first rejection detection module, and the reserved curved surface elements are determined as an initial curved surface element set;
the second-stage rejection detection module 2 is configured to construct respective triangular surface element control networks for the surface elements by using the control vertexes of the surface elements in the initial surface element set, the triangular surface element control networks are plane approximations of the surface elements and completely surround the corresponding surface elements, if a ray does not intersect with a certain triangular surface element control grid, the ray and the surface element corresponding to the triangular surface element control grid do not have an intersection point, the surface element corresponding to the control network is excluded, all the surface elements corresponding to the triangular surface element control grid which does not intersect with the ray are further excluded by using the second rejection detection module, and the reserved surface elements are determined as a target surface element set;
the line-curved surface intersection detection module 3 iteratively solves the intersection point of a certain ray and a certain curved surface element by using an extremum search method: firstly, according to the number k of intersection points of a triangular surface element control network corresponding to a ray and a curved surface element, combining the properties of non-uniform rational B-spline NURBS to obtain an initial value and an iteration region matched with an extreme value search method, and then using the obtained initial value and the iteration region to iteratively solve the intersection points of the curved surface element and the ray by using the extreme value search method; the line-surface intersection detection module 3 further includes an iteration initial value and region selection submodule 31 and an iteration intersection submodule 32, where:
an iteration initial value and area selection submodule 31, configured to select an iteration initial value and an iteration area that are matched with an extremum search method, determine the iteration area by using the number k, which is less than or equal to 2, of intersection points of a triangular surface element control network corresponding to a certain surface element, and combining properties of non-uniform rational B-spline NURBS: if k =1, there are two cases where the ray intersects the surface element: no intersection point exists or only one intersection point exists, the parameter domain of the surface element is directly used as an iteration region, and the parameter value at the center of the iteration region is used as an initial iteration value; if k =2, there are three cases where the ray intersects the surface element: the method comprises the following steps that no intersection point exists, one intersection point exists or two intersection points exist, the parameter domain of the curved surface element is divided into four uniform regions equally and respectively used as iteration regions, and the parameter value of the center of each iteration region is used as an initial iteration value;
the iteration intersection solving submodule 32 is configured to use the iteration initial value and the area obtained by the area selection submodule 31 to apply an extremum search method to iteratively solve an intersection point of a certain curved surface element and a ray: firstly, a ray equation is converted into a form of intersection of two planes, then the form of intersection is combined with a curved surface equation to obtain an objective equation, the solution of the ray-curved surface intersection point can be equivalent to the solution of an objective equation root, and finally the objective equation is solved by iteration by using an extremum search method, wherein the extremum search method is a search type iteration method, has low requirement on an initial value, does not diverge for any given initial value, and iterates in u and v directions respectively.
The trajectory tracking module 4 firstly uses the line-curved surface intersection detection module 3 to iteratively solve the intersection point of a certain ray and a certain curved surface element to obtain all intersection points of the certain ray and all curved surface elements forming the target surface, then uses the geometric relation to find the illuminated intersection point closest to the ray source point, then uses the Fresnel law to obtain the reflection direction of the ray, uses the illuminated intersection point as the starting point and uses the reflected ray as a new incident ray to continue tracking, forms recursion, and thereby realizes the trajectory tracking of the ray.
Referring to fig. 2, the ray tracing method based on NURBS curved surface according to the present invention is implemented as follows:
step 1: the surface is represented as a number of connected surface elements according to the node distance.
Because the number of intersection points of a ray and a curved surface is not a constant with a fixed value, iterative solution of ray-curved surface intersection points can not be directly carried out by using an iterative method, the curved surface is represented as a plurality of connected curved surface elements by using a node distance, and at most two intersection points exist between a ray and a curved surface element according to the property that the NURBS curved surface has the highest continuity in parameter elements, so that the curved surface is represented as a plurality of connected curved surface elements, and the intersection calculation of the ray and the curved surface is simplified into the intersection calculation of the ray and a series of curved surface elements.
First, the mathematical expression of a piece of curved surface patch p × q times is expressed as a vector S (u, v):
wherein u and v are two parameters of NURBS surface, 0 ≦ u, v ≦ 1, P is all control vertices of the surface, ω is weight factor, { N i,p (u) } and { N } j,q (v) The node vectors are defined by the node U and the node V, respectively, the non-rational B spline basis functions, subscripts i and j represent index subscripts of each parameter, i is greater than or equal to 0 and less than or equal to n-1, j is greater than or equal to 0 and less than or equal to m-1, n and m are the numbers of the B spline basis functions in the U and V directions, respectively, p and q are the orders of the B spline basis functions in the U and V directions, respectively, and the node vectors are represented by the node U i And v j Expressed as:
then, an interval formed by two nodes with a non-zero difference is called a node distance, a parameter element is formed by using the node distances in the u and v directions, and a curved surface element is obtained by mapping the parameter element, wherein the mapping relation is shown in fig. 3.
Step 2: and establishing a coordinate axis arrangement bounding box AABB for each curved surface element by using the strong convex hull property of the NURBS curved surface element, excluding all curved surface elements corresponding to the AABB which do not intersect with the rays, and taking the reserved curved surface elements as an initial curved surface element set.
The strong convex hull characteristic of non-uniform rational B-spline NURBS is explained as follows:
if it is not
The curved surface S (u, v) is located at the control point P i,j In a convex hull of which i 0 And j 0 Index indices representing nodes in u and v directions, respectively, i and j represent index indices controlling vertices in u and v directions, respectively, i = i 0 -p,…,i 0 ，j＝j 0 -q,…,j 0 P and q are the order of the B-spline basis function in the u and v directions respectively, [. Cndot. ] represents the node distance, [. Cndot. ] represents the parameter element formed by the node distance in the two directions.
The strong convex hull property of the non-uniform rational B-spline NURBS surface elements is utilized to establish respective coordinate axis arrangement bounding boxes AABB for the surface elements, and a vector Vmax = (x is the maximum value of x, y and z coordinates in all control vertexes of the surface elements is utilized to form a vector Vmax = (x is the maximum value of y and z coordinates in all control vertexes of the surface elements) max ,y max ,z max ) Minimum value composition vector Vmin = (x) min ,y min ,z min ) (ii) a Then, the two vectors are used as diagonal vectors to obtain an AABB bounding box of each curved surface element, and the structure of the bounding box is shown in FIG. 4;
because the curved surface element is contained in the corresponding AABB, if a certain ray does not intersect with a certain AABB, the ray does not have an intersection with the curved surface element contained in the AABB, all the curved surface elements corresponding to the AABB which do not intersect with the ray are excluded, and the reserved curved surface elements are used as an initial curved surface element set.
And step 3: and establishing respective triangular surface element control networks by using the control vertexes of the initial surface elements in the set of surface elements.
3a) Establishing an inner triangular network:
(3a1) Control of vertex { P ] by a curved primitive i,j ,P i+1,j+1 ,P i,j+1 Either { P } or { P } i,j ,P i+1,j ,P i+1,j+1 Constructing inner triangles for the vertices of the triangles, and constructing an inner triangle network of the curved surface element by using all the inner triangles, wherein P represents a control vertex of the curved surface, i and j respectively represent index subscripts of the control vertex in u and v directions, i =0, \8230;, n, j =0, \8230;, m, n and m are the numbers of B spline basis functions in u and v directions respectively;
(3a2) According to the method for constructing the inner triangular network of a certain surface element in the step (3 a 1), the inner triangular network corresponding to each surface element in the initial surface element set is obtained;
3b) Establishing an edge triangular network:
(3b1) Control the vertex { P ] with a certain surface element i,j ,P i+1,j ,P i+1+a,j },{P i,j+q ,P i+1,j+q ,P i+1+a,j+q },{P i,j ,P i,j+1 ,P i,j+1+b Either { P } or { P } i+p,j ,P i+p,j+1 ,P i+p,j+1+b Constructing an edge triangle for the vertex of the triangle, and constructing an edge triangle network of the surface element by using all the edge triangles, wherein a and B respectively represent the increment of index subscripts of the control vertex in the u direction and the v direction, a is less than or equal to p-1, B is less than or equal to q-1, and p and q are the orders of B spline basis functions in the u direction and the v direction respectively;
(3b2) According to the method for constructing the edge triangular network of a certain curved surface element in the step (3 b 1), the edge triangular network corresponding to each curved surface element in the initial curved surface element set is obtained;
3c) Establishing a triangular surface element control network:
the inner triangle networks corresponding to the surface elements and the edge triangle networks jointly form a triangle surface element control network of each surface element, the control network structure is shown in fig. 5, the total number of triangles of the triangle surface element control network of one p × q-order surface sheet is 2pq +2 (p-1) +2 (q-1), the former item corresponds to the number of inner triangles, the latter two items correspond to the number of edge triangles, and p and q are the orders of B spline basis functions in the directions of parameters u and v respectively.
And 4, excluding all the curved surface elements corresponding to the triangular surface element control network which does not intersect with the rays, and taking the reserved curved surface elements as an initial curved surface element set.
Because the triangular surface element control network is approximate to the plane of the surface element, the triangular surface element control network surrounds the corresponding surface element, if a certain ray does not intersect with the triangular surface element control network, the ray does not have an intersection point with the surface element corresponding to the triangular surface element control network, all the surface elements corresponding to the triangular surface element control network which do not intersect with the ray are excluded, and the reserved surface elements are used as a target surface element set.
And 5: and obtaining an intersection point of a certain incident wave ray and a certain curved surface element in the target curved surface element set by using an extremum search iteration method.
5a) Acquiring the number k of intersection points of a triangular surface element control network corresponding to the rays and the curved surface element by using an intersection testing method of the rays and the planar element;
5b) According to different conditions of k, combining the property that the NURBS surface elements have the highest continuity in the node distance, determining an iteration area and an initial iteration value which are matched with an extremum search method:
when k =1, the ray and the surface element may not have an intersection, if there is an intersection, there must be only one intersection, and at this time, the parameter domain of the surface element is directly used as the iteration domain [ u ] i ,u i+1 )×[v j ,v j+1 ) Center of parameter domain
As an initial iteration value;
when k =2, the parameter domain of the surface element needs to be subdivided and then iterated, the parameter domain of the surface element is equally divided into four uniform regions which are respectively used as iteration regions, the parameter coordinates of the middle points of the four uniform regions are used as initial iteration values, and the divided iteration regions are shown in fig. 6;
5c) And (3) applying an extremum search method to iteratively solve the intersection point:
(5c1) And (3) simultaneous rays and a curved surface equation obtain a target equation:
first, the ray is written as two planes intersecting:
wherein, A 1 ，B 1 ，C 1 ，D 1 ，A 2 ，B 2 ，C 2 And D 2 The method comprises the following steps of obtaining different coefficients of two plane equations of a ray intersection formula, and then combining a mathematical expression S (u, v) of a curved surface with the ray intersection formula to obtain a target equation:
wherein, the first and the second end of the pipe are connected with each other,
u and v are two parameters of NURBS curved surface, u is more than or equal to 0, v is less than or equal to 1 ij ，y ij z ij Three Cartesian coordinates, ω, of the control vertex of the curved surface ij Is the weight factor, { N i,p (u) } and { N } j,q (v) The index subscripts i and j respectively represent index subscripts of each parameter in the u and v directions, i is more than or equal to 0 and less than or equal to n-1, j is more than or equal to 0 and less than or equal to m-1, n and m are the number of the B spline base functions in the u and v directions respectively, and p and q are the orders of the B spline base functions in the u and v directions respectively;
(5c2) Solving an objective equation:
writing the target equation in the form of a sum of squares:
the solution of the intersection point of the ray and the curved surface can be equivalent to the solution of the minimum value of the function g (u, v), the minimum value of the function g (u, v) is solved iteratively by using an extremum search iteration method, and the obtained solution is the parameter coordinate of the intersection point of the ray and the curved surface element.
Step 6: and completing ray trajectory tracking.
(6a) Acquiring all intersection points of the ray and all the curved surface elements forming the target by using the method for acquiring the intersection point of the ray of the incident wave and the curved surface element in the step 5;
(6b) Obtaining an illuminated intersection point nearest to a ray source point by utilizing the geometric relation between the ray source point and each intersection point on the curved surface under the rectangular coordinate system;
(6c) Obtaining the reflection direction of the ray by combining the incident direction of the ray according to the Fresnel law;
(6d) And (4) taking the illuminated intersection point obtained in the step (6 b) as a starting point, and taking the reflected ray obtained in the step (6 c) as a new incident ray to continue tracking, so as to form recursion and realize ray trajectory tracking.
The effects of the present invention can be further verified by the following simulation experiments.
The method is used for carrying out ray tracing on the rays on the surface of the target model, and RCS simulation data obtained by using a ray tracing result is used for verifying that the method is short in ray tracing time and high in RCS calculation accuracy. The experimental facility required by the invention is a computer with a C language compiling environment.
1. Experimental simulation conditions:
the simulation calculation is that the CPU is Intel (R) Core (TM) i5, the main frequency is 3.7GHz, and the memory is 8GB. The VisualStudio2017 compilation environment is installed on the Windows7 system.
2. Analysis of experimental contents and experimental results:
experiment one:
setting the frequency of the incident wave of the radar to be 3GHz, and selecting two typical calculation angles
And
the model and the angle are identified in fig. 7, the ray tracing method based on the NURBS curved surface and the conventional curved surface ray tracing method are respectively used for ray tracing on the target, and the tracing time of the two methods is calculated, and the result is shown in table 1.
TABLE 1
As can be seen from Table 1, the calculation time is shorter by using the method of the invention, and the ray tracing of the target is accelerated by the NURBS-based ray tracing method of the invention.
Experiment two:
selecting the frequency of an incident wave of the radar to be 9.375GHz, the incident angle theta from 0 degree to 50 degrees, the coordinate axis and the angle are marked as in FIG. 8, the target is a flat plate model, and the size of the flat plate is as follows: 0.3 m.times.0.3 m. The panel is subjected to ray tracing by using an accurate formula, the method of the invention and a traditional method respectively, and RCS simulation data is obtained by using a ray tracing result, wherein the result is shown in FIG. 8. The result calculated by using the accurate formula is the RCS accurate solution and is used for comparing the accuracy of the result calculated by the method and the accuracy of the result calculated by using the traditional method, and the method which is better in matching degree with the accurate solution in the two methods has higher calculation accuracy.
As can be seen from FIG. 8, the method provided by the invention has higher matching degree with the precise solution, and the intersection point solution is more precise by verifying the ray tracing method provided by the invention.
Claims (5)
1. A NURBS surface-based ray tracing system, comprising:
the first-stage rejection detection module (1) is used for constructing a coordinate axis arrangement bounding box AABB of each curved surface element, if a ray does not intersect with one AABB, the ray does not have an intersection with the curved surface element corresponding to the AABB, the curved surface elements contained in the AABB are excluded, and the reserved curved surface elements are determined as an initial curved surface element set;
the second-stage rejection detection module (2) is used for establishing respective triangular surface element control networks for the surface elements in the initial surface element set, if the ray does not intersect with a certain triangular surface element control grid, the ray does not have an intersection point with the surface element corresponding to the triangular surface element control grid, the surface element corresponding to the control network is excluded, and the reserved surface elements are determined as a target surface element set;
the line-curved surface intersection detection module (3) is used for solving the intersection points of the curved surface elements and the rays corresponding to the triangular surface element control network in an iterative manner by using an extremum search method, namely, according to the number k of the intersection points of the rays and the certain triangular surface element control network, and by combining the properties of non-uniform rational B-spline NURBS (non-uniform rational B-spline), the initial value and the iteration area matched with the extremum search method are obtained, and then the intersection points of the curved surface elements and the rays corresponding to the triangular surface element control network are solved in an iterative manner by using the obtained initial value and the iteration area;
and the trajectory tracking module (4) is used for selecting the illumination intersection point closest to the ray source point, obtaining the reflection direction of the ray by applying Fresnel law, taking the illuminated intersection point as a starting point, and taking the reflected ray as a new incident ray to continue tracking to form recursion, thereby realizing the ray trajectory tracking.
2. The system according to claim 1, wherein the line-surface intersection detection module (3) comprises:
an iteration initial value and area selection submodule (31) for selecting an iteration initial value and an iteration area matched with an extremum search method, determining the iteration area by utilizing the number k of intersection points of rays and a certain triangular surface element control network, wherein k is less than or equal to 2 and combining the property of non-uniform rational B-spline NURBS: if k =1, directly taking a parameter domain of the corresponding surface element of the triangular surface element control network as an iteration area, and taking a parameter value at the center of the iteration area as an initial iteration value; if k =2, uniformly dividing the parameter domain of the curved surface element into four regions respectively serving as iteration regions, and taking the parameter value at the center of each iteration region as an initial iteration value;
and the iteration intersection solving sub-module (32) is used for utilizing the iteration initial value and the area obtained by the area selection module to iteratively solve the intersection point of the curved surface element and the ray corresponding to the triangular surface element control network by applying an extremum searching method.
3. A ray tracing method based on NURBS curved surface, comprising:
1) According to the nodal distance information of the non-uniform rational B-spline NURBS curved surface, the NURBS curved surface is represented as a plurality of connected NURBS curved surface elements;
2) Establishing a coordinate axis arrangement bounding box AABB (array of bounding boxes) for each curved surface element by utilizing the strong convex hull property of the NURBS curved surface element, if an incident wave ray does not intersect with the AABB bounding box, the ray does not have an intersection with the curved surface element corresponding to the AABB bounding box, excluding the curved surface element contained in the AABB bounding box, and determining the reserved curved surface element as an initial curved surface element set;
3) Establishing respective triangular surface element control networks by utilizing control vertexes of all the surface elements in the initial surface element set, if an incident wave ray does not intersect with a certain triangular surface element control grid, the ray does not have an intersection point with the surface element corresponding to the triangular surface element control grid, excluding the surface element corresponding to the control network, and determining the reserved surface element as a target surface element set;
4) Obtaining the intersection point of a certain incident wave ray and a certain curved surface element by using an extremum search iteration method:
4a) Acquiring the number k of intersection points of a triangular surface element control network corresponding to the rays and the curved surface element by using an intersection testing method of the rays and the planar element, wherein k is less than or equal to 2;
4b) According to different conditions of k, combining the property that the NURBS surface elements have the highest continuity in the node distance, determining an iteration area and an initial iteration value which are matched with an extremum search method:
4b1) When k =1, the ray and the surface element have at most one intersection point, and the parameter domain of the surface element is directly used as an iteration domain [ u [ u ] ] i ,u i+1 )×[v j ,v j+1 ) Center of parameter domain
As initial iteration values, where u and v are two parameters of NURBS surfaceAnd u is more than or equal to 0, v is less than or equal to 1, subscripts i and j represent node coordinates of the parameters, i is more than or equal to 0 and less than or equal to n-1, j is more than or equal to 0 and less than or equal to m-1, n, m is the number of B spline basis functions in u and v directions, [. Cndot.) represents a node distance, and [. Cndot. ] represents a parameter element consisting of the node distances in two directions;
4b2) When k =2, the parameter domain of the surface element needs to be subdivided and then iterated: equally dividing the parameter domain of the curved surface element into four regions respectively as iteration regions, and taking the parameter values of the midpoints of the four regions as initial iteration values;
4c) According to the obtained initial iteration value and the iteration area, an extremum searching method is applied to iteratively solve the intersection point of the ray and the curved surface element corresponding to the triangular surface element control network;
5) According to 4) the method for obtaining the intersection point of a certain incident wave ray and a certain curved surface element, all intersection points of the ray and all curved surface elements forming the target are obtained, then the illuminated intersection point closest to the ray source point is obtained by utilizing the geometric relation, the reflection direction of the ray is obtained by applying the Fresnel law, then the illuminated intersection point is used as the starting point, the reflected ray is used as a new incident ray to continue tracking, the recursion is formed, and the ray trajectory tracking is realized.
4. The method of claim 3, wherein the step of 2) establishing respective coordinate Axis Alignment Bounding Boxes (AABB) for each surface element by using the strong convex hull property of NURBS surface elements comprises using the maximum value of x, y, z coordinates of all control vertices of each surface element to form a vector Vmax = (x is the x-x coordinate of all control vertices of each surface element =) max ,y max ,z max ) Minimum value composition vector Vmin = (x) min ,y min ,z min ) And then the two vectors are used as diagonal vectors to obtain the AABB bounding boxes of the curved surface elements.
5. The method of claim 3, wherein 3) establishing respective triangular bin control networks using the control vertices of each surface element in the initial set of surface elements is performed by:
3a) Establishing an inner triangular network:
3a1) Control of vertex { P ] by a curved primitive i,j ,P i+1,j+1 ,P i,j+1 } or { P i,j ,P i+1,j ,P i+1,j+1 Constructing inner triangles for the vertices of the triangles, and constructing an inner triangle network of the surface element by using all the inner triangles, wherein P represents a control vertex of the surface, i and j respectively represent index subscripts of the control vertex in the u and v directions, i =0, \8230, n, j =0, \8230, m, n and m are the number of B spline basis functions in the u and v directions respectively;
3a2) Obtaining an inner triangular network corresponding to each curved surface element in the initial curved surface element set according to the method for constructing the inner triangular network of a certain curved surface element in the step 3a 1);
3b) Establishing an edge triangular network:
3b1) Control of vertex { P ] by a curved primitive i,j ,P i+1,j ,P i+1+a,j },{P i,j+q ,P i+1,j+q ,P i+1+a,j+q },{P i,j ,P i,j+1 ,P i,j+1+b Either { P } or { P } i+p,j ,P i+p,j+1 ,P i+p,j+1+b Constructing an edge triangle for the vertex of the triangle, and constructing an edge triangle network of the curved surface element by using all the edge triangles, wherein a and B respectively represent the increment of index subscripts of the control vertex in the u and v directions, a is less than or equal to p-1, B is less than or equal to q-1, and p and q are the orders of B-spline basis functions of parameters in the u and v directions;
3b2) Constructing a method of an edge triangular network of a certain curved surface element according to the 3b 1), and obtaining the edge triangular network corresponding to each curved surface element in the initial curved surface element set;
3c) Establishing a triangular surface element control network:
the triangular surface element control network of each surface element is formed by the inner triangular network and the edge triangular network corresponding to each surface element.
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